How do you differentiate #f(x)= (x^2+1)(x^3+1) # using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Sasha P. Dec 16, 2015 #f'(x) = 5x^4 + 3x^2 + 2x# Explanation: #f'(x) = (x^2+1)' * (x^3+1) + (x^2+1)(x^3+1)' # #f'(x) = 2x(x^3+1) + (x^2+1)*3x^2# #f'(x) = 2x^4+2x +3x^4+3x^2# #f'(x) = 5x^4 + 3x^2 + 2x# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 1507 views around the world You can reuse this answer Creative Commons License